Yes! This is getting very browsable/fun to explore.

Auto-tagging/making clickable certain proper nouns like Homelander could be neat if there’s a way to detect them.

Since sexual themes are heavily regulated or prohibited in most cultures, such a word may fail to exist, or to survive intact through the millennia. I suppose that local metaphoric and slang words, and contextually-altered expressions (like the generic "daydream" narrowed to that sense) replace it in many / most cases.

Same with words for copulation (highly restricted) and even for wooing / courting, which are also pretty universal activities since times immemorial.

Yes, it doesn't, but that's your answer because there is no single, exclusive English word for sexually desiring someone. So there can't really be one that exclusively refers to sexually fantasizing about them, at least, not until the age of extensive psychological and sociological taxonomies.

My response to your finding it difficult to believe is: you're asking for a word for an intensely private act! Think about how rarely people overtly and bluntly say they are sexually fantasizing about someone. When it's actually admitted to, it's done using a variety of metaphors, slang and indirect hints.

And in general, we don't have a commonly used prefix or second compounded word to turn a physical act into a fantasy. Even though "fuck" predates Early Modern there was nothing commonly attached to it to make it mental.

In my experience, modern English adopts idioms more often than new words. "Sexual fantasy" is a common term for what you're asking about. It may sound too dry and basic to be an idiom, but remember that English is packed, filled, stuffed, and choked with synonyms. That most people say "sexual fantasy" points to it being an idiom. "Dirty thoughts" would be a close contender.

If you really want a single verb, "lust."

For sexual fantasies about somebody one's looking at, "undressing with one's eyes."